This paper discusses the mathematical aspects of ill-posed problems in early vision, which are inverse problems that often lack uniqueness, stability, or continuity. Early vision involves tasks like motion recovery, shape from shading, and edge detection, all of which require solving inverse problems. These problems are typically ill-posed, meaning they may not have a unique solution or may be unstable to small changes in input data. The paper reviews regularization theory, which provides methods to stabilize and solve such problems. It introduces the concept of generalized inverses and discusses various regularization techniques, including Tikhonov regularization and stochastic regularization. The paper also explores the application of these methods to specific problems in early vision, such as edge detection, optical flow, and surface interpolation. It emphasizes the importance of considering the statistical properties of signals and noise in regularization methods, and introduces a Bayesian approach that connects regularization with Markov Random Field models. The paper concludes by highlighting the role of regularization in ensuring the stability and robustness of solutions to ill-posed problems in early vision.This paper discusses the mathematical aspects of ill-posed problems in early vision, which are inverse problems that often lack uniqueness, stability, or continuity. Early vision involves tasks like motion recovery, shape from shading, and edge detection, all of which require solving inverse problems. These problems are typically ill-posed, meaning they may not have a unique solution or may be unstable to small changes in input data. The paper reviews regularization theory, which provides methods to stabilize and solve such problems. It introduces the concept of generalized inverses and discusses various regularization techniques, including Tikhonov regularization and stochastic regularization. The paper also explores the application of these methods to specific problems in early vision, such as edge detection, optical flow, and surface interpolation. It emphasizes the importance of considering the statistical properties of signals and noise in regularization methods, and introduces a Bayesian approach that connects regularization with Markov Random Field models. The paper concludes by highlighting the role of regularization in ensuring the stability and robustness of solutions to ill-posed problems in early vision.